In this paper, novel harvesting systems are proposed and studied to obtain enhanced energy from transient waves. Each of these systems contains a piezo-lens to focus waves and a harvester to yield energy from the induced focused waves. The piezo-lens comprises a host plate and piezoelectric patches bonded on the plate surfaces. The piezoelectric patches are shunted with negative capacitance (NC) circuits in order to control the spatial variation of the effective refractive index inside the piezo-lens domain. The harvester is placed at the designed focal point of the piezo-lens, two different synchronized switch harvesting on inductor (SSHI) based harvesters are analyzed in the studies. Corrected reduced models are developed to predict the transient responses of the harvesting systems. The performances of the systems incorporating SSHI-based harvesters in transient wave energy harvesting are studied and compared with the system using a standard DC harvester. The focusing effect of the piezo-lens on transient waves and its capability to improve the harvested energy are verified. Since the NC circuits are active elements, an energy balance analysis is performed. Applicability of the harvesting systems is also discussed.